OR-AND-invert
From Wikipedia, the free encyclopedia
OR-AND-invert gates, or OAI-gates, are logic gates comprising OR gates followed by a NAND gate. They can be efficiently implemented in logic families like CMOS and TTL. They are dual to AND-OR-invert gates.
Overview
OR-AND-invert gates implement the inverted product of sums. groups of , input signals combined with OR, and the results then combined with NAND.
Examples
2-1 OAI-gate

A 2-1-OAI gate realizes the following function:
Truth table 2-1 OAI | |||
Input A B C | Output Y | ||
0 | 0 | 0 | 1 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
2-2 OAI gate
A 2-2-OAI gate realizes the following function:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle Y = \overline{(A \lor B) \land (C \lor D)} }
Truth table 2-2 OAI | ||||
INPUT A B C D | OUTPUT Q | |||
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 |
0 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 1 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
Realization

OAI-gates can efficiently be implemented as complex gates. An example of a 3-1 OAI-gate is shown in the figure below.[1]
Examples of use
One possibility of implementing an XOR gate is by using a 2-2-OAI-gate with non-inverted and inverted inputs. [2]

References
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